Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Consider a $4 \times 4$ matrix A with rows ${\vec{v}}_{1}, {\vec{v}}_{2}, {\vec{v}}_{3}, {\vec{v}}_{4}$ . If , find the determinants in Exercises 11 through 16.

12. localid="1659509477853" $d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}]$

Therefore, the determinant of given determinant matrix is given by,

$d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}] = - 8$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition

A determinant is a unique number associated with a square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

Step 2: Given

Given determinant,

$\det (A) = 8 \det [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}]$

Step 3: To find determinant

To determine,

$d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}] = - d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}] d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}] = - d e t (A) . d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}] = - 8$

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Linear Algebra With Applications

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Short Answer

Consider a $4 \times 4$ matrix A with rows ${\vec{v}}_{1}, {\vec{v}}_{2}, {\vec{v}}_{3}, {\vec{v}}_{4}$ . If , find the determinants in Exercises 11 through 16.

12. localid="1659509477853" $d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}]$

Step by Step Solution

Step 1: Definition

Step 2: Given

Step 3: To find determinant

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Linear Algebra With Applications

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Short Answer

Consider a 4×4 matrix A with rows v→1,v→2,v→3,v→4. If , find the determinants in Exercises 11 through 16. 12. localid="1659509477853" det[v→1v→2v→3v→4]

Step by Step Solution

Step 1: Definition

Step 2: Given

Step 3: To find determinant

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Pure Maths

Consider a $4 \times 4$ matrix A with rows ${\vec{v}}_{1}, {\vec{v}}_{2}, {\vec{v}}_{3}, {\vec{v}}_{4}$ . If , find the determinants in Exercises 11 through 16.

12. localid="1659509477853" $d e t [\begin{matrix} {\vec{v}}_{1} \\ {\vec{v}}_{2} \\ {\vec{v}}_{3} \\ {\vec{v}}_{4} \end{matrix}]$